Pronouns that end with -self refer back to the subject of the sentence. They are called intensive pronouns when they emphasize the role of the subject. You can see this usage in a phrase like “as I myself have argued.” They are called reflexive pronouns when they are the object of the action the subject has done, as in “I pride myself on my writing skills” or “She cut herself off from cigarettes.”
But sometimes you’ll see these pronouns used as replacements for personal pronouns such as “me” or “I.” There’s usually no reason to do this.
Consider the following sentence: “If you have any questions, just ask myself or one of my colleagues.” There is no “I” for “myself” to refer back to. The pronoun “me” is the proper object of “ask”: “just ask me or one of my colleagues.” Another example: “The only ones in attendance were myself and one of my friends.” The word “myself” has no other noun or pronoun to intensify or reflect. So “myself” should be “I,” and you might want to rephrase the sentence altogether: “My friend and I were the only ones in attendance.”
Here’s a more subtle example: “The problem with his play is that it’s all about himself.” This sounds natural to me, but note that there’s no “he” for “himself” to refer back to. Experts are divided over whether this kind of usage is acceptable (Copperud 257). “His play” might imply the existence of a “he” for “himself” to refer back to, and so some writers consider this usage to be standard. However, some might object, and there would be nothing wrong with changing “himself” to “him.”
In general, if you can substitute another form of the pronoun for the form ending in –self, it’s a good idea to do so.
Copperud, Roy H. American Usage and Style: The Consensus. Van Nostrand Reinhold, 1980.